고체역학 (Beer) — Transformations of Stress and Strain: Problem 7.148

7.148 Show that the sum of the three strain measurements made with a 60° rosette is independent of the orientation of the rosette and equal to \[ \epsilon_1 + \epsilon_2 + \epsilon_3 = 3\epsilon_{\text{avg}} \] where \( \epsilon_{\text{avg}} \) is the abscissa of the center of the corresponding Mohr’s circle.